HDOJ 6608 Fansblog

题目链接
Problem Description
Farmer John keeps a website called ‘FansBlog’ .Everyday , there are many people visited this blog.One day, he find the visits has reached P , which is a prime number.He thinks it is a interesting fact.And he remembers that the visits had reached another prime number.He try to find out the largest prime number Q ( Q < P ) ,and get the answer of Q! Module P.But he is too busy to find out the answer. So he ask you for help. ( Q! is the product of all positive integers less than or equal to n: n! = n * (n-1) * (n-2) * (n-3) *… * 3 * 2 * 1 . For example, 4! = 4 * 3 * 2 * 1 = 24 )

Input
First line contains an number T(1<=T<=10) indicating the number of testcases.
Then T line follows, each contains a positive prime number P (1e9≤p≤1e14)

Output
For each testcase, output an integer representing the factorial of Q modulo P.

Sample Input
1
1000000007

Sample Output
328400734

• 题意
  给你一个素数p，q为小于它的最大素数，求q！%p

• 思路
  显然题目可以分成两部分，1是求q，2是求q！%p。
  对1部分，最简单的做法就是从p-1开始向下枚举至第一个素数，对于一个足够大的素数n，不超过n的素数大约有n/ln n个即每ln n个数中大约有一个素数，故需要枚举的数量不超过100。
  对于2部分，直接求解最多优化到O（nlogn），加上1部分必然会超时。考虑威尔逊定理：对于素数p，有（p-1）！ 三 -1（mod p），故可以直接从（p-1）！开始推至q。
  -代码

#include<bits/stdc++.h>
#define ll long long
using namespace std;
__int128 _a, _b, _m;
long long mul (long long a, long long b, long long m) {//防止爆ll
	_a = a, _b = b, _m = m;
	return (long long)(_a * _b % _m);
}
ll ex_gcd(ll a, ll b, ll &x, ll &y) {
    if (b == 0) {
        x = 1, y = 0;
        return a;
    }
    else {
        ll r = ex_gcd(b, a % b, y, x);
        y -= x * (a / b);
        return r;
    }
}
ll inv(ll a, ll n) {
    ll x, y;
    ex_gcd(a, n, x, y);
    x = (x % n + n) % n;
    return x;
}
inline bool check (long long n) {
	for (long long i = 2; i * i <= n; i++) {
		if (n % i == 0) return true;
	}
	return false;
}
int main(){
    ll p,q,ans;
    int t;
    scanf("%d",&t);
    while(t--){
        scanf("%I64d",&p);
        ans=p-1;
        q=p-1;
        while(check(q)){
                ans=mul(inv(q,p),ans,p);
            q--;
        }
        printf("%I64d\n",ans);
    }
}

标签：prime,return,ll,number,long,素数,Fansblog,6608,HDOJ
来源： https://blog.csdn.net/weixin_43883326/article/details/97768082